Violation of the fluctuation-dissipation theorem for fast superdiffusion

TL;DR

This paper investigates anomalous diffusion in one-dimensional systems, revealing that fast superdiffusion violates the fluctuation-dissipation theorem and introduces an effective temperature linked to metastability in complex systems.

Contribution

It demonstrates the violation of the fluctuation-dissipation theorem in fast superdiffusion and connects this to the concept of an effective temperature and metastability.

Findings

Fast superdiffusion violates the fluctuation-dissipation theorem.

An effective temperature emerges in systems exhibiting fast superdiffusion.

Metastability is associated with the violation in complex systems.

Abstract

We study anomalous diffusion for one-dimensional systems described by a generalized Langevin equation. We show that superdiffusion can be classified in normal superdiffusion and fast superdiffusion. For fast superdiffusion, we prove that the Fluctuation-Dissipation Theorem does not hold, which induces an effective temperature in the system. This effective temperature is a signature of metastability found in many complex system such as Spin-Glass and granular material.